Question

A man has some shares of Rs. 100 par value paying 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% Rs. 50 shares at a premium of Rs. 10. This transaction decreases his income from dividends by Rs. 120. Calculate:

1. the number of shares before the transaction.
2. the number of shares he sold.
3. his initial annual income from shares.

Answer 1

Let no. of shares = x

Value of x shares = x × 100 = 100x

and dividend = `(100x xx 6)/(100)` = Rs. 6x

and dividend on half-shares = `"Rs." (6x)/(2)` = Rs. 3x

Now, no of shares he sold out = `x/(2)`

Amount received at 10% discount

= `x/(2) xx 90` = Rs. 45x

In investing Rs. 45x, no. of share he purchased = `(45x)/(60)`

∴ Amount of shares = `(45x)/(60) xx 50 = "Rs." (225x)/(6)`

Income at the rate of 7% = `(225)/(6)x xx (7)/(100) = (21x)/(8)`

Differece in income = `3x - (21x)/(8) = (3x)/(8)`

According to the condition, `(3x)/(8)` = 120.

⇒ x = `(120 xx 8)/(3)` = 320

i. No. of share he hold initially = 320

ii. No. of share he hold later = `(320)/(2)` = 160

iii. Amount of income initially

= 320 × 6

= Rs. 1920